ppft-py 0.1.0

Highly optimized Pseudo-Polar Fourier Transform in Python

ppft-py

Highly optimized Pseudo-Polar Fourier Transform in Python.

This repository provides a Python implementation of the Pseudo-Polar Fourier Transform (PPFT) in both 2D (PPFT2D) and 3D (PPFT3D), based on the methods presented in the following papers:

• Averbuch et al., 2001 — Fast Slant Stack: A notion of Radon Transform for Data in a Cartesian Grid which is Rapidly Computable, Algebraically Exact, Geometrically Faithful and Invertible.
• Averbuch & Shkolnisky, 2003 — 3D Fourier based discrete Radon transform, Applied and Computational Harmonic Analysis, Vol. 15, No. 1, pp. 33–69.

Features

• GPU-accelerated computation for enhanced performance.
• Backend-agnostic implementation using the Array API Standard with no direct dependencies.
• Memory-efficient and fully vectorized modes available.
• Optimized handling of real-valued input data for improved efficiency.
• Supports additional FFT backends using SciPy for extended flexibility and performance.

Usage

To transform data with the Pseudo-Polar Fourier Transform, import the function from ppftpy and apply it to the input data:

2D Pseudo-Polar Fourier Transform:

import numpy as np

from ppftpy import ppft2

data = np.random.default_rng().random((128, 128))

transformed = ppft2(data)

3D Pseudo-Polar Fourier Transform:

import numpy as np

from ppftpy import ppft3

data = np.random.default_rng().random((32, 32, 32))

transformed = ppft3(data)

Note: The example uses NumPy arrays for the Pseudo-Polar Fourier Transform. However, this library supports all backends that implement the Array API Standard and its FFT extension (via the array-api-compat compatibility layer). See backends for a list of tested backends.

SciPy FFT Backends

Additionally, implementations of the SciPy FFT interface can be used as backends for the underlying FFT:

2D Pseudo-Polar Fourier Transform with SciPy backend:

import numpy as np

from ppftpy import ppft2

data = np.random.default_rng().random((128, 128))

transformed = ppft2(data, scipy_fft=True)

2D Pseudo-Polar Fourier Transform with pyFFTW backend:

import numpy as np
import pyfftw.interfaces.scipy_fft as pyfftw
from scipy import fft

from ppftpy import ppft2

data = np.random.default_rng().random((128, 128))

with fft.set_backend(pyfftw):
    transformed = ppft2(data, scipy_fft=True)

Note: For more information on using custom FFT backends with SciPy, check out the backend control section of the SciPy documentation. See backends for a list of tested backends.

Backends

The following implementations of the Array API Standard have been tested to work:

Backend	Devices	Minimum Version
NumPy	CPU	1.23.0
CuPy	GPU	10.0.0
DPNP	CPU / GPU	0.17.0[^1]
Dask	CPU / GPU	2024.8.1
PyTorch	CPU / GPU	1.13.0
JAX	CPU / GPU	0.4.32

[^1]: Released, but not yet available on PyPI.

The following implementations of the SciPy FFT interface have been tested to work:

Backend	Supports	Minimum Version
SciPy	NumPy (incl. Dask/JAX with NumPy arrays)	1.8.0
mkl_fft	NumPy (incl. Dask/JAX with NumPy arrays)	1.3.6
pyFFTW	NumPy (incl. Dask/JAX with NumPy arrays)	0.13.0
CuPy	CuPy (incl. Dask with CuPy arrays)	10.0.0

Acknowledgments

This project utilizes concepts from the reference implementations and for generating test data for regression tests:

• PPFT2D: ShkolniskyLab/PPFT2D
• PPFT3D: ShkolniskyLab/PPFT3D and its associated MATLAB Central resource